Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.2 - Trigonometric Functions of Real Numbers - 5.2 Exercises - Page 417: 34

Answer

$\sin{t} = \frac{2\sqrt5}{5}$ $\cos{t} = \frac{\sqrt5}{5}$ $\require{cancel}\tan{t} = 2$

Work Step by Step

RECALL: For the terminal point P(x, y) on a unit circle, $\sin{t} = y, \cos{t} = x, \text{ and } \tan{t} = \frac{y}{x}, x\ne0$ Use the formulas above to obtain: $\sin{t} = \frac{2\sqrt5}{5}$ $\cos{t} = \frac{\sqrt5}{5}$ $\require{cancel}\tan{t} = \dfrac{\frac{2\sqrt5}{5}}{\frac{\sqrt5}{5}} = \dfrac{2\sqrt5}{5} \cdot \left(\dfrac{5}{\sqrt5}\right)=\dfrac{2\cancel{\sqrt5}}{\cancel{5}} \cdot \left(\dfrac{\cancel{5}}{\cancel{\sqrt5}}\right)=2$
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